Splash function for the collision of sand-sized particles onto an inclined granular bed, based on discrete-element-simulations

Abstract

This work is motivated by the lack of a model for the splash function associated with the collision of wind-blown sand grains onto an inclined granular surface. This splash function, which describes the velocity of rebound particles and the number and velocity of ejected particles, is an essential ingredient of theoretical models of sand transport and the formation of dunes and ripples. While previous models regarded the granular bed as a horizontal surface, there is experimental evidence that bed slopes can affect the splash process. However, since it is difficult to investigate particle trajectories near the bed from experiments, numerical simulations that resolve individual particle trajectories provide useful means to elucidate the effect of bed slope on the splash function. Here we employ numerical simulations by means of the Discrete-Element-Method (DEM) to investigate the splash function of sand-sized particles impacting onto inclined beds. To this end, we consider bed slopes consistent with those of the windward side of ripples and dunes. Specifically, the angle θ between the granular bed and the horizontal is varied from 0° to 15°, while a broad range of particle impact velocities (from 1 m/s to 7 m/s) is considered. Moreover, we consider values of incident particle diameter din within the range 120 ≤ din/μm ≤ 520, i.e., consistent with natural sand. We obtain expressions for all parameters of the splash function as a function of the incident particle diameter and velocity, and the bed slope. In particular, our simulations show that the effect of the bed slope on the splash function depends on the size of the impacting particle, which has implication for grain trajectories formative of ripples and dunes.